Dark Photon and Muon $g-2$ Inspired Inelastic Dark Matter Models at the High-Energy Intensity Frontier

We study hidden-sector particles at past (CERN-Hamburg-Amsterdam-Rome-Moscow Collaboration and NuCal), present (NA62, SeaQuest, and DarkQuest), and future (LongQuest) experiments at the high-energy intensity frontier. We focus on exploring the minimal vector portal and the next-to-minimal models in which the productions and decays are decoupled. These next-to-minimal models have mostly been devised to explain experimental anomalies while avoiding existing constraints. We demonstrate that proton fixed-target experiments provide one of the most powerful probes for the MeV to few GeV mass range of these models, using inelastic dark matter (iDM) as an example. We consider an iDM model with a small mass splitting that yields the observed dark matter relic abundance, and a scenario with a sizable mass splitting that can also explain the muon $g-2$ anomaly. We set strong limits based on the CERN-Hamburg-Amsterdam-Rome-Moscow Collaboration and NuCal experiments, which come close to excluding iDM as a full-abundance thermal dark matter candidate in the MeV to GeV mass range. We also make projections based on NA62, SeaQuest, and DarkQuest and update the constraints of the minimal dark photon parameter space. We find that NuCal sets the only existing constraint in $\epsilon \sim {10}^{-8}–{10}^{-4}$ regime, reaching $\sim 800\mathrm{MeV}$ in dark photon mass due to the resonant enhancement of proton bremsstrahlung production. These studies also motivate LongQuest, a three-stage retooling of the SeaQuest experiment with short ($\lesssim 5\mathrm{m}$), medium ($\sim 5\mathrm{m}$), and long ($\gtrsim 35\mathrm{m}$) baseline tracking stations and detectors as a multipurpose machine to explore new physics.

Figure 1

We show updates on the kinetically mixed visibly decaying dark photon constraints and projections. In (a), gray contours are the previous bounds set based on analyses of the NuCal [51, 54] and CHARM [53] experiments. In (b), projections for future experiments are shown in dot-dashed curves with color and also labeled in the plot. In both (a) and (b), our updated bounds on CHARM (purple) and NuCal (blue) and our new projections of NA62 (red) and LongQuest-I (black) are shown. (a) Updates on dark photon bounds and the NA62 projection. (b) Compilation of projections and constraints on dark photon.

Figure 2

We show new constraints on iDM based on the data of CHARM (purple) and NuCal (blue), and the projected sensitivity of the NA62 beam-dump run (red). The gray shaded regions are previously existing constraints (see Sec. I B). We also include the potential E137 decay constraint [10, 13, 40] along with future projections [10, 13, 32, 73, 76, 77, 85, 122, 123, 124, 125, 126, 127, 128, 129, 130]. One can see the E137, Mini Booster Neutrino Experiment, and Beam Dump Experiment (BDX) projections are already covered by CHARM and NuCal. (a) Compilation of constraints and sensitivity projections for iDM with $m_{A^{\prime }}=3m_1$, ${\alpha }_D=0.1$, and $\mathrm{\Delta }=0.1$.

Figure 3

These plots show constraints and sensitivity projections for iDM within the muon $g-2$ motivated regime. Here we consider $m_{A^{\prime }}=3m_1$ for demonstration. The muon $g-2$ favored regime is the light-green band in (a), while the thick-black curves are again the parameter contour yielding the correct DM relic abundance. We considered the bounds from CHARM (purple) and NuCal (blue) and projections from NA62 [${10}^{18}$ POT (red), $1.3\times {10}^{16}$ POT (magenta)], SQ-DQ [${10}^{20}\mathrm{POT}$ (dashed-cyan), $1.4\times {10}^{18}\mathrm{POT}$ (dashed-pine green), and LongQuest-I (3-GeV cut: darker green; no-cut: black)]. In (b), we only plot the LongQuest-I no cut curve because it is basically identical to the 3-GeV cut result. The gray region denotes the previously existing constraints. (a) iDM: $\mathrm{\Delta }=0.4$, ${\alpha }_D=0.1$. With muon $g-2$ and DM regimes. (b) iDM Muon $g-2$ Target: $\mathrm{\Delta }=0.5$, $\mathrm{\epsilon }={\mathrm{\epsilon }}_{{(g-2)}_{\mu }}$.